A high speed turbo machine, such as, for example, a steam or gas turbine, generally comprises a plurality of blades arranged in axially oriented rows, the rows of blades being rotated in response to the force of a high pressure fluid flowing axially through the machine. Due to their complex design, natural resonant mechanical frequencies of the blades may coincide with or be excited by certain blade rotational speeds and rotational harmonics thereof. To prevent excessive vibration of the blade about its normal position, prudent design practice dictates that the blades be constructed such that the frequencies of the lowest modes fall between harmonics of the operating frequency of the turbine. In addition, the blades may be excited by non-synchronous forces such as aerodynamic buffeting or flutter. In order to avoid the vibration exceeding certain levels and setting up objectionable stresses in the blades, it is common to monitor the vibrations of the blades, both during the design and testing of the turbine and during normal operation of the turbine. For example, it is known to use non-contacting proximity sensors or probes to detect blade vibrations. The probes detect the actual time-of-arrival of each blade as it passes each probe and provide corresponding signals to a blade vibration monitor system (BVM). The BVM processes the signals from the probes to determine vibration levels of the blades, including vibration amplitude, frequency and phase shift. See, for example, the vibration monitoring machines described in U.S. Pat. Nos. 4,593,566, 4,887,468, 4,896,537 and 5,148,711, which patents are incorporated herein by reference.
While the BVM and similar systems applying Fourier analysis provide useful information for analyzing blade vibrations, the blade vibration wave is typically under-sampled, where inadequate data is available to provide resolution of the blade vibration frequencies. This limitation is presently overcome by adding additional, equally spaced probes and associated signal channels to the BVM. However, installing additional probes is expensive and may be physically difficult to implement in that it is generally not possible to install all of the additional spaced probes at equal spacing, nor is it generally possible to position all the probes in the same plane, such that each probe may sample a different location on the blade tip which may result in an error and spectral noise in the measurement.
The expense and difficulties in positioning plural probes may be avoided by using one probe and implementing computer modeling of the blade to unfold the one-probe Fourier spectra and identify the vibration mode. That is, the unfolding process produces numerous possible blade frequencies, and computer modeling may be implemented to select the best fit unfolded frequency. However, the one-probe configuration provides an under-sampled approach, and computer models of the blades do not accurately predict the influence of temperature, centrifugal force loading and untwist on blade mode resonance frequencies.
In an alternative approach, a sine function curve fit (SFCF) based approach may be used to analyze the blade vibrations. In this approach, five to eight probes may be positioned so as to optimize one particular blade mode, or to best optimize a group of modes. The SFCF approach involves intensive calculations and is typically limited to the case where only a single mode is excited at any one time, in that the analysis is indeterminate if two or more modes are excited.